by G S Hall (University of Aberdeen, UK)

Table of Contents (116k)
Preface (65k)
Chapter 1: Introduction (494k)

This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.

• Introduction
• Algebraic Concepts
• Topology
• Manifold Theory
• Lie Groups
• The Lorentz Group
• Space-Times and Algebraic Classification
• Holonomy Groups and General Relativity
• The Connection and Curvature Structure of Space-Time
• Affine Vector Fields on Space-Time
• Conformal Symmetry in Space-Times
• Projective Symmetry in Space-Times
• Curvature Collineations